Question

Find the annual percent increase or decrease that y = 0.35(2.3)x models. (1 point) A.230% increase B.130% increase C.30% decrease D.65% decrease

Answer 1

Answer: B. 130% increase

Step-by-step explanation:

Given function :  $y=0.35(2.3)^x$

If x represents the number of years, we have to determine the two values of y in consecutive terms to determine if the value of y increases or decreases after a year.

This function is equivalent to the exponential growth function

$y=A(1+r)^x$, where A=0.35 and (1+r)=2.3, [A= initial amount , r=annual percent increase]

Thus,

$\Rightarrow\ r=2.3-1\\\Rightarrow\ r=1.3\\\Rightarrow\ r=1.3\times100\%=130\%$

Hence, the annual percent increase is 130%.

Answer 2

The annual percent of the model $y = 0.35{\left( {2.3}\right)^x}$ is increases by $\boxed{130\% }$. Option (B) is correct.

Further explanation:

The exponential growth function or compound interest formula can be expressed as follows,

$\boxed{A = C{{\left( {1 + i} \right)}^x}}$

Here, A represents the total amount, C represents the initial amount, irepresent the annual percentage increase and x represents the time.

Given:

The annual percentage model can be expressed as,

$y = 0.35{\left( {2.3} \right)^x}$

The options of annual percentage are given as follows.

A. $230\% {\text{ increases}}.$

B. $130\% {\text{ increases}}.$

C. $30\% {\text{ decreases}}.$

D. $65\% {\text{ decreases}}.$

Explanation:

Compare given model $y = 0.35{\left( {2.3} \right)^x}$ with the exponent growth model $y = 0.35{\left( {2.3}\right)^x}.$

The value of C is 0.35 and the value of $\left( {1 + i} \right)$ is 2.3.

$\begin{aligned}1 + i&= 2.3\\i &=2.3 - 1\\i &= 1.3\\\end{aligned}$

The function is increases by $130\%.$

Option A is not correct.

Option B is correct.

Option C is not correct.

Option D is not correct.

Hence, the annual percent of the model $y = 0.35{\left( {2.3}\right)^x}$ is increases by $\boxed{130\% }$. Option (B) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Investment

Keywords: Annual percentage, increases or decreases, model, interest rate, simple interest, compound interest, annual payment, annuity.